A paper company dumps nondegradable waste into a river that flows by the firm's plant. The firm estimates its production function to be:Q = 6KW,where Q = annual paper production measured in pounds, K = 6W MP W = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. a. Determine the firm's optimal ratio of waste water to capital. b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee? class=answers-bank-image d-inline rel=preload of capital, and K = 6W MP W = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. a. Determine the firm's optimal ratio of waste water to capital. b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee? class=answers-bank-image d-inline rel=preload of polluted water dumped into the river per year. The marginal products of capital and labor are given as follows:MP K = 6W MP W = 6KThe firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year.a. Determine the firm's optimal ratio of waste water to capital.b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce?c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee?

Question

A paper company dumps nondegradable waste into a river that flows by the firm's plant. The firm estimates its production function to be:Q = 6KW,where Q = annual paper production measured in pounds,  K  = 6W MP W  = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. a. Determine the firm's optimal ratio of waste water to capital. b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee? class=answers-bank-image d-inline rel=preload > of capital, and  K  = 6W MP W  = 6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year. a. Determine the firm's optimal ratio of waste water to capital. b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce? c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee? class=answers-bank-image d-inline rel=preload > of polluted water dumped into the river per year. The marginal products of capital and labor are given as follows:MP K  = 6W MP W  = 6KThe firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates a $30 per hour rental rate on capital. The operating budget for capital and waste water is $300,000 per year.a. Determine the firm's optimal ratio of waste water to capital.b. Given the firm's $300,000 budget, how much capital and waste water should the firm employ? How much output will the firm produce?c. The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped. Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ? How much will the firm pay in effluent fees? What happens to the firm's cost as a result of the effluent fee?

Mounika Uppala · Accepted Answer

Final Answer : a.MP W  = 6KMP K  = 6WMRTS =  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > =  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > Rate of water charge to price of capital:  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > =  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > = .25Equating MRTS to ratio of input prices  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > = 0.25, K = 0.25Wb.C = P W W + P K K300,000 = 7.50W + 30KRecall K = 0.25W300,000 = 7.5W + 30(0.25W)300,000 = 7.5W + 7.5WW = 20,000 gallonsK = 0.25WK = 0.25(20,000)K = 5000Q = 6(5000)(20,000)Q = 600,000,000c.P W  becomes $15 (7.50 previous cost + effluent fees).Ratio of input price is  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > =  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > = 0.5MRTS =  W  = 6K MP K  = 6W MRTS =   =   Rate of water charge to price of capital:   =   = .25 Equating MRTS to ratio of input prices   = 0.25, K = 0.25W b.C = P W W + P K K 300,000 = 7.50W + 30K Recall K = 0.25W 300,000 = 7.5W + 30(0.25W) 300,000 = 7.5W + 7.5W W = 20,000 gallons K = 0.25W K = 0.25(20,000) K = 5000 Q = 6(5000)(20,000) Q = 600,000,000 c.P W  becomes $15 (7.50 previous cost + effluent fees). Ratio of input price is   =   = 0.5 MRTS =   Hold Q constant at 600,000,000 Q = 6KW K = 0.5W 600,000,000 = 6(0.5W)(W) 600,000,000 = 3W 2   200,000,000 = W 2      W = 14,142.13 or W = 14,142 K = 0.5(14,142) K = 7071 Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071. Effluent fee is 7.5 × 7071 = $53,032.5 Cost prior to effluent fee was $300,000 (from isocost level) Cost after effluent fee is C = P W W + P K K where P W  = 15 (including fee) P K  = 30 C = 15(14142) + 30(7071) C = 212,130 + 213,130 C = $424,260 Cost rises from $300,000 to $424,260. class=answers-bank-image d-inline rel=preload > Hold Q constant at 600,000,000Q = 6KWK = 0.5W600,000,000 = 6(0.5W)(W)600,000,000 = 3W 2  200,000,000 = W 2    W = 14,142.13 or W = 14,142K = 0.5(14,142)K = 7071Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071.Effluent fee is 7.5 × 7071 = $53,032.5Cost prior to effluent fee was $300,000 (from isocost level)Cost after effluent fee isC = P W W + P K Kwhere P W  = 15 (including fee)P K  = 30C = 15(14142) + 30(7071)C = 212,130 + 213,130C = $424,260Cost rises from $300,000 to $424,260.

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